application problem

Question

If there were 12 more blue marbles the number of blue marbles would be double the number of red. If there were 4 less red marbles, the number of green marbles would be double that of red. There are 100 marbles total. How many red ones? I have to write and equation.

Answer 1

B: # of blue marbles 

R: # of red marbles

G: # of green marbles 

 

(B+12) =2* R

(R-4)*2=G

G+ R+ B= 100

 

Solve the first two equations in terms of R and plug them into the third equation. 

 

(B+12)=2*R 

subtract 12 from both sides 

B+12-12=2R-12 -> B= 2R-12

 

(R-4)*2=G

distribute the 2 

2R-8=G

 

Plug these equations into the third equation for the terms B and G

G+ R+ B=100

(2R-8)+R+ (2R-12)=100

 

Combine like terms 

2R+R+2R=5R

-8-12= -20

 

5R-20=100

Add 20 to both sides 

5R-20+20=100+20

5R=120

divide both sides by 5 

5R/5=120/5 

R=24